NONLINEAR ADAPTIVE SIGNAL-PROCESSING BASED ON RATIONAL-FUNCTION

While linear adaptive filters are useful in a large number of applicat ions and relatively simple from the conceptual and implementational po int of view, there are many practical situations that require nonlinea r processing. This paper presents a novel adaptive nonlinear filter wh ich derives its nonlinearity by using rational functions. The output o f this nonlinear system is related to its inputs through a finite orde r rational function. The rational function structure is attractive in adaptive filtering since it is a universal approximator and the coeffi cients of the filter can be estimated using a linear adaptive algorith m. Two representative examples from signal processing, classification and prediction, are used to demonstrate capabilities of this nonlinear adaptive filter that are lacking in its linear counterpart. The poten tial uses for this nonlinear adaptive filter will be further demonstra ted by discussing the problem that is often encountered in the real wo rld, namely, the estimation of directions-of-arrival (DOA) of two clos ely spaced signals using a uniform array and time series modeling. For the first problem, a new high resolution method using a rational func tion is derived and standard simulation examples are given. For the la tter, real-life radar data are used as a test for the rational functio n filter in the practical application. In both cases, the results that are obtained using this nonlinear adaptive filter are encouraging.